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Wittaler [7]
1 year ago
10

Find the value or measure. Assume all lines that appear to be tangent are tangent. X=

Mathematics
1 answer:
aev [14]1 year ago
7 0

According to the secant-tangent theorem, we have the following expression:

(x+3)^2=10.8(19.2+10.8)

Now, we solve for <em>x</em>.

\begin{gathered} x^2+6x+9=10.8(30) \\ x^2+6x+9=324 \\ x^2+6x+9-324=0 \\ x^2+6x-315=0 \end{gathered}

Then, we use the quadratic formula:

x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}

Where a = 1, b = 6, and c = -315.

\begin{gathered} x_{1,2}=\frac{-6\pm\sqrt[]{6^2-4\cdot1\cdot(-315)}}{2\cdot1} \\ x_{1,2}=\frac{-6\pm\sqrt[]{36+1260}}{2}=\frac{-6\pm\sqrt[]{1296}}{2} \\ x_{1,2}=\frac{-6\pm36}{2} \\ x_1=\frac{-6+36}{2}=\frac{30}{2}=15 \\ x_2=\frac{-6-36}{2}=\frac{-42}{2}=-21 \end{gathered}<h2>Hence, the answer is 15 because lengths can't be negative.</h2>
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The combustion of one gallon of automobile fuel produces about 5 pounds of carbon (in CO₂). Two autos are making a trip of 600 m
rewona [7]

Answer:

Approximately 50 pounds less carbon (in CO₂) will be produced by the second auto on this trip.

Step-by-step explanation:

We have been given that the combustion of one gallon of automobile fuel produces about 5 pounds of carbon (in CO₂). Two autos are making a trip of 600 miles.

Let us find amount of fuel used by autos by dividing the total distance by their mileage.

\text{Fuel used by 1st auto}=\frac{\text{ 600 miles}}{\frac{\text{ 20 miles}}{\text{gallon}}}

\text{Fuel used by 1st auto}=\frac{\text{ 600 miles}}{\text{ 20 miles}}\times \text{gallon}

\text{Fuel used by 1st auto}=30 \text{ gallons}

\text{Fuel used by 2nd auto}=\frac{\text{ 600 miles}}{\frac{\text{ 30 miles}}{\text{gallon}}}

\text{Fuel used by 2nd auto}=\frac{\text{ 600 miles}}{\text{ 30 miles}}\times \text{gallon}

\text{Fuel used by 2nd auto}=20 \text{ gallons}

Let us find the difference of fuel used by both autos.

\text{Number of gallons that 2nd auto used less than 1st auto}=30-20

\text{Number of gallons that 2nd auto used less than 1st auto}=10

Since one gallon of automobile fuel produces about 5 pounds of carbon, so 10 gallons of fuel will produces 5\times 10=50 pounds of carbon.

Since 2nd auto used 10 gallons less than 1st auto, therefore, 2nd auto will produce 50 pounds less carbon than 1st auto.

8 0
3 years ago
The restaurant served 220 sandwiches, 120tacos, and 160 salads for lunch. What is the ratio of salads to total number of lunches
sladkih [1.3K]

Answer:

8 to 25

Step-by-step explanation:

The total number of lunches sold i

220+120+160 =500

We want the ratio of salads to total lunches

salads: lunches

160:    500

Divide each side by 20

160/20 : 500/20

8:25

3 0
3 years ago
To which set or sets does the number 8.25 belong
Tpy6a [65]

Rational sets also known as ratios

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3 years ago
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23. Starting with x=0.81818181 , express x as a fraction in simplest form.
White raven [17]
You could do x=81 with the little line on the top (represents the number going on forever, and example is 0.818181818181818181818181818818181818 etc.)
6 0
3 years ago
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6% sales tax, hotel charges $265 find cost before tax?
Mama L [17]
265 x 0.06 = 15.9

265 - 15.9 = 249.1

249.1 is your answer

hope this helps
3 0
3 years ago
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